Somehow or other, you either need a plugin for OBS that does that (search in
https://obsproject.com/forum/search/?type=resource&c[categories][0]=6 ), or you need a separate app that can drive a sound card. Send that app to one that you're not using, and point OBS's Desktop Capture or Audio Output Capture to that same device.
For a more complex rig, there's this handy little tool:
VoiceMeeter Banana, the Advanced Virtual Audio Mixer by V.Burel
vb-audio.com
VoiceMeeter Potato, the Ultimate Virtual Audio Mixer for Windows
vb-audio.com
Two different sizes of the same thing, that put a small mixing console between some virtual sound cards, in addition to also connecting to physical ones itself. Connect other apps to those virtual sound cards, and it works as if you had a physical console connected to that many physical sound cards.